The number of mosquitoes in Minneapolis, Minnesota (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by: $m(x)=-(x-5)^2+25$ How many centimeters of rainfall will produce the maximum number of mosquitoes?
Explanation: The number of mosquitoes is modeled by a quadratic function, whose graph is a parabola. The maximum number of mosquitoes is reached at the vertex. So in order to find when that happens, we need to find the vertex's $x$ -coordinate. The function $m(x)$ is given in vertex form. The vertex of $-(x-{5})^2{+25}$ is at $({5},{25})$. In conclusion, $5$ centimeters of rainfall will produce the maximum number of mosquitoes.